Chapter R.CT, Problem 1CT

To determine

To find:

Whether the statement $B\text{'} = \{2, 4, 6, 8\}$ is true or false.

Answer to Problem 1CT

Solution:

The given statement is false.

Explanation of Solution

Concept:

1) The set is a collection of objects.

The objects that belong to the sets are their elements or their members.

All the elements are separated by comma.

For example {1, 2, 3}.

1) The set is a collection of objects.

The objects that belong to the sets are their elements or their members.

All the elements are separated by comma.

For example {1, 2, 3}.

2) Let A and B are two sets, with universal set U.

The complement of set A is A′ with all elements of U except the elements belong to the set A.

That is, A′ = {x/x $\in U, x\notin A$}

For example, let U = {1, 2, 3, 5, 7, 9} and A = {1, 3} then A′= {2, 5, 7, 9}

Calculation:

Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A= {1, 2, 3, 4, 5, 6}, B = {1, 3, 5}, C = {1, 6}, and D = {4}.

B′ = {x/x $\in U, x\notin B$}

So, $B^{\text{'}}=U-B$

And, $B^{\text{'}}=\{2,\mathrm{ }4,\mathrm{ }6,\mathrm{ }7,\mathrm{ }8\}$

But it is given that B' = {2, 4, 6, 8}.

So, given statement is false.

Final statement:

Therefore, the given statement is false.